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The maximum distance between n points in three dimensions can occur no more than 2n-2 times. Also, there exists a fixed number c such that no distance determined by a set of ...

In its simplest form, the principle of permanence states that, given any analytic function f(z) defined on an open (and connected) set U of the complex numbers C, and a ...

A subfield which is strictly smaller than the field in which it is contained. The field of rationals Q is a proper subfield of the field of real numbers R which, in turn, is ...

For a group G and a normal subgroup N of G, the quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called ...

Let G be a finite, connected, undirected graph with graph diameter d(G) and graph distance d(u,v) between vertices u and v. A radio labeling of a graph G is labeling using ...

Ramsey's theorem is a generalization of Dilworth's lemma which states for each pair of positive integers k and l there exists an integer R(k,l) (known as the Ramsey number) ...

In a noncommutative ring R, a right ideal is a subset I which is an additive subgroup of R and such that for all r in R and all a in I, ar in I. (1) For all a in R, the set ...

The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

In n dimensions for n>=5 the arrangement of hyperspheres whose convex hull has minimal content is always a "sausage" (a set of hyperspheres arranged with centers along a ...

A class of subvarieties of the Grassmannian G(n,m,K). Given m integers 1<=a_1<...<a_m<=n, the Schubert variety Omega(a_1,...,a_m) is the set of points of G(n,m,K) ...